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The passive resonance frequencies of the flute were measured with high precision and compared with the frequencies obtained by blowing. The differences, which vary from +20 to −25 cents over the scale, are wholly accounted for by air temperature and composition and by variation of coverage of the mouth hole. No frequency pulling due to the blowing mechanism was observed. Measurements of frequency and radiated power using an artificial blowing mechanism provide an explanation for the variations in lip configuration observed in photographs. The tapered head joint provides a partial compensation for lip-coverage variation, but irregularities in the resonant column give marked departures from calculated frequencies based on a smooth tube.
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John W. Coltman (1966) studied this question.
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